The solubility product of `Hg_(2)I_(2)` is equal to

Options

A. `[Hg_(2)^(2+)][I^(-)]`
B. `[Hg^(2+)][I^(-)]`
C. `[Hg_(2)^(2+)][I^(-)]^(2)`
D. `[Hg^(2+)][I^(-)]^(2)`

Explanation

To find the solubility product (Ksp) of \( \text{Hg}_2\text{I}_2 \), we will follow these steps:

### Step 1: Write the dissociation equation
The first step is to write the dissociation equation for \( \text{Hg}_2\text{I}_2 \). When \( \text{Hg}_2\text{I}_2 \) dissolves in water, it dissociates into mercury ions and iodide ions:

\[ \text{Hg}_2\text{I}_2 (s) \rightleftharpoons \text{Hg}_2^{2+} (aq) + 2 \text{I}^- (aq) \]

### Step 2: Identify the ions and their stoichiometric coefficients
From the dissociation equation, we can identify the ions produced and their stoichiometric coefficients:
- For \( \text{Hg}_2^{2+} \), the coefficient is 1.
- For \( \text{I}^- \), the coefficient is 2.

### Step 3: Write the expression for the solubility product (Ksp)
The solubility product \( K_{sp} \) is defined as the product of the molar concentrations of the ions, each raised to the power of their respective coefficients in the balanced equation. Therefore, we can write:

\[ K_{sp} = [\text{Hg}_2^{2+}]^1 \times [\text{I}^-]^2 \]

### Step 4: Final expression for Ksp
Substituting the coefficients from the dissociation equation into the expression for \( K_{sp} \):

\[ K_{sp} = [\text{Hg}_2^{2+}] \times [\text{I}^-]^2 \]

This is the final expression for the solubility product of \( \text{Hg}_2\text{I}_2 \).

### Conclusion
Thus, the solubility product \( K_{sp} \) of \( \text{Hg}_2\text{I}_2 \) is given by:

\[ K_{sp} = [\text{Hg}_2^{2+}] \times [\text{I}^-]^2 \]